Question

Question 1

The ACME Fuel Company is testing three gasoline additives that potentially improve miles per gallon (mpg). Data on the mpg increases are below.

Additive 1	Additive 2	Additive 3
6.54924242494422	10.8272118564027	16.3965138498227
8.60769443033187	8.67299309375278	13.8264401852561
5.05391921558221	8.21238247050848	6.331782806765
2.96796467314839	11.0822837448977	10.4506468121659
7.97810063172781	8.59019087696806	21.8235410521825
7.46392482343272	10.5572062252476	10.2801885874108
10.536239276453	9.74063701358136	15.8806047473296
9.28918796384799	7.70761387370591	13.7481769824239
5.11534958765997	10.3504957013572	10.6078180738212
8.68885423370508	9.29383878407116	10.8479260147142

a) For each of the three additives, make boxplots, probability plots,
run Anderson-Darling tests, and Shapiro-Wilks tests to check for
normality.

b) Based on the results in part (a), which test (Hartley’s F-max,
Bartlett’s, Levene’s) is best to use to check for a difference
between the variances of mpg increases for the three additives?

c) Run the test you suggested in part (b). Be sure to state the null
and alternative hypotheses, test statistic, p-value, and conclusion.

Answer 1

(a) The boxplot is:

Additive 1 Additive3 Additive2

The probability plots are:

For Additive 1:

Normal Q-Q Plot of Additive1 Expected Normal Value 1012 Observed Value

For Additive 2:

Normal Q-Q Plot of Additive2 Expected Normal Value 11 10 Observed Value

For Additive 3:

Normal Q-Q Plot of Additive3 Expected Normal Value 10 20 Observed Value

The normality test results are:

Tests of Normality Kolmogorov-Smirnova Statistic df Sig. Statistic Additive 1 .141 10 2009 963 Additive 2 163 10 2009 941 Additive 3 193 10 200* 943 *. This is a lower bound of the true significance. a. Lilliefors Significance Correction Shapiro-Wilk df - 10 - 10 10 Sig. 822 .564 .590

(b) The best test to use to check for a difference between the variances of mpg increases for the three additives is Hartley’s F-max test.

(c) The hypothesis being tested is:

H₀: µ₁ = µ₂ = µ₃

H₁: At least one means is not equal

The SPSS output is:

ANOVA Type Sum of Squares df Mean Square sig 10.096 .001 Between Groups Within Groups Total 170.423 227.880 398.302 85.211 8.440

The test statistic is 10.096.

The p-value is 0.001.

Therefore, we can conclude that there is a difference between the variances of mpg increases for the three additives.

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